“He is very, very capable of taking a top job.”
Celtic are on the lookout for a permanent managerial appointment after Neil Lennon was sacked last month.
O’Neill believes that the Celtic hierarchy are “missing a trick” by not considering Keane for the job.
The Hoops have endured a miserable league campaign, throwing away their chance to win a 10th successive Scottish Premiership title after nine years of dominance.
Celtic have dropped points in 13 games this season compared to just five for the Gers, leaving them 20 points behind Steven Gerrard’s team at the top of the table.
As a result of their disappointing displays, the club saw fit to sack Lennon in February and they are yet to name a permanent replacement for the Northern Irishman.
Back in 2006, Keane spent the last six months of his playing career with the Hoops after arriving at the club from Man United.
The ex-Nottingham Forest man would then announce his retirement from the sport in June of the same year.
Martin O’Neill on Keane.
“What you see is what you get from Roy,” O’Neill said.
“My own personal view is that I think owners and Chief Executives are missing a trick by not thinking about him as becoming a manager, that’s my view.
“I think he has learned a great, great deal and I think he is very, very capable of taking a top job.
“There is time for them to develop, you have to think about winning again, and who would give you the chance to go and win again.
“Rangers are on the up at this moment, they’re entitled to, they haven’t been there in a long, long time.
“So who can give Celtic to get that momentum again, to go and win.”